The road to Utopia is the road to Hell. — Communism and socialism are the opiates of the intelligentsia. — The left, in its eternal and futile quest for "equality", is more than willing to abolish liberty and sunder fraternity.

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Probability, Existence, and Creation: A Footnote

[H]umans invent mathematical concepts by way of abstracting elements from the world around them—shapes, lines, sets, groups, and so forth—either for some specific purpose or simply for fun. They then go on to discover the connections among those concepts. Because this process of inventing and discovering is man-made—unlike the kind of discovery to which the Platonists subscribe—our mathematics is ultimately based on our perceptions and the mental pictures we can conjure….

[W]e adopt mathematical tools that apply to our world—a fact that has undoubtedly contributed to the perceived effectiveness of mathematics. Scientists do not choose analytical methods arbitrarily but rather on the basis of how well they predict the results of their experiments….

Not only do scientists cherry-pick solutions, they also tend to select problems that are amenable to mathematical treatment. There exists, however, a whole host of phenomena for which no accurate mathematical predictions are possible, sometimes not even in principle. In economics, for example, many variables—the detailed psychology of the masses, to name one—do not easily lend themselves to quantitative analysis. The predictive value of any theory relies on the constancy of the underlying relations among variables. Our analyses also fail to fully capture systems that develop chaos, in which the tiniest change in the initial conditions may produce entirely different end results, prohibiting any long-term predictions. Mathematicians have developed statistics and probability to deal with such shortcomings, but mathematics itself is limited, as Austrian logician Gödel famously proved….

This careful selection of problems and solutions only partially accounts for mathematics’s success in describing the laws of nature. Such laws must exist in the first place! Luckily for mathematicians and physicists alike, universal laws appear to govern our cosmos: an atom 12 billion light-years away behaves just like an atom on Earth; light in the distant past and light today share the same traits; and the same gravitational forces that shaped the universe’s initial structures hold sway over present-day galaxies. Mathematicians and physicists have invented the concept of symmetry to describe this kind of immunity to change….

I started with two basic, interrelated questions: Is mathematics invented or discovered? And what gives mathematics its explanatory and predictive powers? I believe that we know the answer to the first question. Mathematics is an intricate fusion of inventions and discoveries. Concepts are generally invented, and even though all the correct relations among them existed before their discovery, humans still chose which ones to study. The second question turns out to be even more complex. There is no doubt that the selection of topics we address mathematically has played an important role in math’s perceived effectiveness. But mathematics would not work at all were there no universal features to be discovered. You may now ask: Why are there universal laws of nature at all? Or equivalently: Why is our universe governed by certain symmetries and by locality? I truly do not know the answers, except to note that perhaps in a universe without these properties, complexity and life would have never emerged, and we would not be here to ask the question. (“Why Math Works,” Scientific American, August 2, 2011)

Comments & Correspondence

Now that this blog is in hiatus, I have closed comments on all posts. If you wish to communicate privately, you may e-mail me at the Germanic nickname for Friedrich followed by the last name of the great Austrian economist and Nobel laureate whose first name is Friedrich followed by the 3rd and 4th digits of his birth year followed by the usual typographic symbol followed by the domain and extension for Google’s e-mail service — all run together.

On Liberty and Libertarianism

What is liberty? It is peaceful, willing coexistence and its concomitant: beneficially cooperative behavior.

John Stuart Mill opined that "the only purpose for which power can be rightfully exercised over any member of a civilized community, against his will, is to prevent harm to others." But who determines whether an act is harmful or harmless? Acts deemed harmless by an individual are not harmless if they subvert the societal bonds of trust and self-restraint upon which liberty itself depends.

Which is not to say that all social regimes are regimes of liberty. Liberty requires voice -- the freedom to dissent -- and exit -- the freedom to choose one's neighbors and associates. Voice and exit depend, in turn, on the rule of law under a minimal state.

Liberty, because it is a social phenomenon and not an innate condition of humanity, must be won and preserved by an unflinching defense of a polity that fosters liberty through its norms, and the swift and certain administration of justice within that polity. The governments in and of the United States have long since ceased to foster liberty, but most Americans are captives in their own land and have no choice but to strive for the restoration of liberty, or something closer to it.

Who can restore liberty? Certainly not the self-proclaimed libertarians who are fixated on Mill's empty harm principle and align with the left on social norms. Traditional (i.e., Burkean) conservatism fosters the preservation and adherence of beneficial norms (e.g., the last six of the Ten Commandments). Thus, by necessity, the only true libertarianism is found in traditional conservatism. I am a traditional conservative, which makes me a libertarian -- a true one.

Notes about Usage

“State” (with a capital “S”) refers to one of the United States, and “States” refers to two or more of them. “State” and “States,” thus used, are proper nouns because they refer to a unique entity or entities: one or more of the United States, the union of which, under the terms and conditions stated in the Constitution, is the raison d’être for the nation. I reserve the uncapitalized word “state” for a government, or hierarchy of them, which exerts a monopoly of force within its boundaries.

Marriage, in the Western tradition, predates the state and legitimates the union of one man and one woman. As such, it is an institution that is vital to civil society and therefore to the enjoyment of liberty. The recognition of a more-or-less permanent homosexual pairing as a kind of marriage is both ill-advised and illegitimate. Such an arrangement is therefore a “marriage” (in quotation marks) or, more accurately, a homosexual cohabitation contract (HCC).

The words “liberal”, “progressive”, and their variants are usually enclosed in quotation marks (sneer quotes) because they refer to persons and movements whose statist policies are, in fact, destructive of liberty and progress. I sometimes italicize the words, just to reduce visual clutter.

I have reverted to the British style of punctuating in-line quotations, which I followed 40 years ago when I published a weekly newspaper. The British style is to enclose within quotation marks only (a) the punctuation that appears in quoted text or (b) the title of a work (e.g., a blog post) that is usually placed within quotation marks.

I have reverted because of the confusion and unsightliness caused by the American style. It calls for the placement of periods and commas within quotation marks, even if the periods and commas don’t occur in the quoted material or title. Also, if there is a question mark at the end of quoted material, it replaces the comma or period that might otherwise be placed there.

If I had continued to follow American style, I would have ended a sentence in a recent post with this:

What a hodge-podge. There’s no comma between the first two entries, and the sentence ends with an inappropriate question mark. With two titles ending in question marks, there was no way for me to avoid a series in which a comma is lacking. I could have avoided the sentence-ending question mark by recasting the list, but the items are listed chronologically, which is how they should be read.

This not only eliminates the hodge-podge, but is also more logical and accurate. All items are separated by commas, commas aren’t displaced by question marks, and the declarative sentence ends with a period instead of a question mark.